Mathematical neuroscience is required to understand the normal functions of the computational brain. As a corollary, we can translate our fundamental understanding of the nervous system to better understand and treat disorders of the brain. There are a variety of brain diseases that are considered dynamical - where the symptoms are consequences of pathological parameters of the underlying neuronal elements and network. Several dynamical diseases have steadily improving mechanistic understanding, embodied into computational models that increasingly reflect the dynamics of the disease symptoms. These include Parkinson's disease and epilepsy. We suspect that other more complex brain diseases are revealing a dynamical component, such as depression and schizophrenia. Along with the advent of improving with computational models, the technical ability to perform open or closed loop deep brain stimulation is now becoming increasingly applied to treat these dynamical diseases. Thus as we better understand dynamical disease, the ability to dynamically probe and control them is now at hand. Another area of medical application of mathematical theory is in the area of brain interfaces. Here, measurement arrays (electrodes or optical) can be used to extract dynamics from ensembles of neurons, and functions are created to decode such information. Such decodings enable us to understand the neural code, and to drive robotic devices or encode information to stimulate the brain. In addition to devices that can adapt to the brain's activity, it is now clear that the brain co-adapts to such devices - learning to use them to accomplish tasks. The cutting edge of interfacing with decoding from and encoding information for the brain is an important cutting edge of mathematical biosciences. Lastly, genomic variability is an inherent aspect of the robustness of species --- it is the plausibility of life itself. Yet the dynamical expression of genomic variability may remain within, or branch across species boundaries --- speciation requires a phenotypic dynamical expression. In neuronal circuits, there is substantial variation in the levels of active channel proteins, and computationally, there are wide varieties of building equivalent dynamics from available genetic protein products. In epilepsy, there is increasing evidence that the combinatorics of multiple channel protein variations may contribute to producing similar expression of the dynamics of epilepsy. In depression, the autoreceptors and reuptake transporters on dopaminergic and serotonergic neurons change their expression levels in response to long-term changes in extracellular concentrations of neurotransmitters. Thus understanding the mechanisms by which SSRIs work necessarily involves understanding gene regulation, biochemistry, and electrophysiology, and how they influence each other dynamically in neurons. We will explore the intersection of evolution, genetic variability, and dynamical disease.

Accepted Speakers

Maxim Bazhenov

The Salk Inst. for Biological Studies

Rafal Bogacz

Computer Science, University of Bristol

Markus Dahlem

Otto-von-Guericke University Magdeburg

Rhonda Dzakpasu

Physics, Georgetown University

Uri Eden

Mathematics and Statistics, Boston University

Flavio Frohlich

Psychiatry, University of North Carolina, Chapel Hill

David Grayden

Eletrical & Electronic Engineering, The University of Melbourne

Yixin Guo

Department of Mathematics, Drexel University

Robert Kass

Department of Statistics, Carnegie-Mellon University

Mark Kramer

Math and Stats, Boston University

Michelle McCarthy

Mathematics and Statistics, Boston University

Cameron McIntyre

Department of Biomedical Engineering, Case Western Reserve University

Tay Netoff

Biomedical Engineering, University of Minnesota

Duane Nykamp

School of Mathematics, University of Minnesota

Michael Reed

Mathematics, Duke University

Leonid Rubchinsky

Department of Mathematical Sciences and Stark Neurosciences Research Institute at the Indiana University School of Medicine, Indiana University--Purdue University

Prominent beta frequency oscillations appear in the basal ganglia of Parkinsons disease patients. The dynamical mechanisms by which these beta oscillations arise are unknown. Using mathematical models, we show that robust beta frequency rhythms can emerge from inhibitory interactions between striatal medium spiny neurons. Our modeling studies propose that the pathologic beta oscillations in Parkinsons disease may arise as an indirect effect of striatal dopamine loss on the striatal cholinergic system. Experimental testing of our model by infusion of the cholinergic agonist carbachol into normal, mouse striatum induced pronounced, reversible beta oscillations in the striatal local field potential. These results suggest the prominent beta oscillations in Parkinsons disease may bethe result of an exaggeration of normal striatal network dynamics.

In Parkinson's disease, increased power of oscillations in firing rate has been observed throughout the cortico-basal-ganglia circuit. In particular, the excessive oscillations in the beta range (13-30Hz) have been shown to be associated with difficulty of movement initiation. However, on the basis of experimental data alone it is difficult to determine where these oscillations are generated, due to complex and recurrent structure of the cortico-basal-ganglia-thalamic circuit. This talk will describe a computational model of a subset of basal-ganglia that is able to reproduce experimentally observed patterns of activity. The analysis of the model suggests where and under which conditions the beta oscillations are produced.

Deep brain stimulation (DBS) has emerged as an exciting new possibility for the treatment of neuropsychiatric disorders. Theoretical and experimental evidence suggest that when DBS is applied to neural tissue, it responds with the generation of action potentials in axons. This is especially pertinent to neuropsychiatric DBS applications because they are currently focused on stimulation of sub-cortical white matter. Unfortunately, it is unclear which specific pathways within the white matter are responsible for generating therapeutic benefit from the stimulation. We are attempting to identify those pathways via creation of patient-specific computational models that combine diffusion-tensor tractography, axonal stimulation predictions, and clinical outcome analyses. Our early results from patients with treatment refractory depression suggest that pathways associated with the ventral medial pre-frontal cortex and accumbens play an important role in therapeutic benefit. Identification of specific target pathways for modulation provides opportunities to improve clinical selection of electrode placement and stimulation settings for DBS devices.

03:15 PM 04:00 PM

Yixin Guo - A model of thalamocortical relay neuron and the parkinsonian network

We study a data-driven model of thalamocortical (TC) relay neuron to examine the TC relay responses to an excitatory input train, under inhibitory signals. We first incorporate recording data as inhibitory signals to the TC model to investigate the mechanism underlying deep brain stimulation (DBS) which has been proven clinically effective to relieve motor symptoms for Parkinsonian patients. Then we explore the closed-loop stimulation paradigm using a parkinsonian network model of the basal-ganglia thalamocortical circuit. Our computational results show that the type of stimulation, based on a filtered version of the local field potential, significantly improves the fidelity of thalamocortical (TC) relay. To further understand the different scenarios of TC relay responses, we analyze the entrainment of the TC neuron to periodic signals that alternate between 'on' and 'off', respectively. By exploiting invariant sets of the system and their associated invariant fiber bundles that foliate the phase space, we reduce the 3D TC model to a 2D map. Based on this map, we reproduce the possible scenarios of TC relay responses observed in the data-driven model.

Robert Kass - A Framework for Statistical Evaluation of Neural Synchrony

Several authors have discussed previously the use of loglinear models, often called maximum entropy models, for analyzing spike train data to detect synchrony. The usual loglinear modeling techniques, however, do not allow for time-varying firing rates that typically appear in stimulus-driven (or action-driven) neurons, nor do they incorporate non-Poisson history effects or covariate effects. I will outline a generalization of the usual approach, which combines point process regression models of individual-neuron activity with loglinear models of multiway synchronous interaction (Kass, Kelly, and Loh, 2011, Annals of Applied Statistics; Kelly and Kass, 2012, Neural Computation). I will also describe a method, based on Bayesian control of false discoveries, for assessing the large number of pairs of neurons that are typically examined in a single experiment. Preliminary physiological results come from Utah array recordings in V1.

12:30 PM 02:00 PM

Lunch Break

02:00 PM 02:45 PM

John Terry

03:15 PM 04:00 PM

Mark Kramer - Multi-scale seizure dynamics

A seizure represents an extreme deviation from normal brain activity. In this talk, we will consider some characteristics of the seizure as observed across spatial and temporal scales in human patients. We will focus specifically on changes in the rhythmic voltage activity, and consider techniques to characterize these changes. We will also discuss a mathematical model consistent with the stereotyped dynamics observed at seizure termination, and use this model to propose what happens dynamically when a seizure fails to self- terminate.

Michael Reed - Serotonin and the mysteries of depression and SSRI action

Despite decades of research, the biochemical and neurophysiological causes of depression remain unknown. Furthermore, although selective serotonin reuptake inhibitors (SSRIs) block the reuptake of serotonin and alleviate depression in some patients, it is not clear how or why they work. Mathematical models of serotonin synthesis, release, and reuptake can shed light on the control mechanisms of the serotonin system and suggest hypotheses about the action of SSRIs. We will discuss two of the standard hypotheses and propose a new hypothesis.

Parkinson?s disease has been traditionally thought of as a dopaminergic disease in which cells of the substantia nigra pars compacta (SNc) die. However, accumulating evidence implies an important role for the serotonergic system in Parkinson?s disease in general and in physiological responses to levodopa therapy, the first line of treatment. We use a mathematical model to investigate the consequences of levodopa therapy on the serotonergic system and on the pulsatile release of dopamine (DA) from dopaminergic and serotonergic terminals in the striatum.

We will also ask, and propose an answer to, the question of what serotonin is doing in the striatum anyway?

Ionic concentrations fluctuate significantly during seizures. Substantial increase of extracellular K+ is found during electrically- or pharmacologically-induced paroxysmal activity, along with increase of intracellular Na+. These changes of the ionic concentrations trigger various homeostasis mechanisms such as glial uptake and Na+/K+ ATPase. While Na+/K+ ATPase is one of the most studied proteins, its role in epilepsy remains unclear. Using computational model of in vivo epileptiform activity, we found that increase of intracellular Na+ during epileptiforms leads to significant activation of Na+/K+ ATPase; this increase mediates hyperpolarizing current by Na+/K+ pump that contributes to termination of seizure and postictal depression state. Deficiencies of the Na+/K+ ATPase promote continuous epileptiform activity. In terms of dynamics, the mechanism underlying the smooth transition is due to a safe bifurcation of a homoclinic orbit of a saddle-node equilibrium state terminating the quiescence period of bursting. Overall, our study demonstrated a complex role played by Na+/K+ ATPase in developing of epileptiform activity and may suggest new targets for antiepileptic drugs.

Motor symptoms of Parkinson's disease have been associated with the synchronized oscillatory activity in the cortico-basal ganglia-thalamic circuits. Here we will present our observations of the patterns of synchronized activity obtained through simultaneous intraoperative recordings of spikes and LFP in the basal ganglia and cortical EEG in parkinsonian patients. We discuss the temporal patterning of the observed synchronized patterning. We show how the synchronization of EEG in motor and prefrontal areas (which can be obtained noninvasively) is predictive of the spike-LFP synchrony in subthalamic nucleus. We also consider the observed phenomena within the framework of mathematical models of cortico-basal ganglia circuits.

Transient dynamics is pervasive in the human brain and poses challenging problems both in mathematical tractability and clinical observability. We investigate statistical properties of transient cortical wave patterns with characteristic forms (shape, size, duration) in a canonical reaction-diffusion model with mean field inhibition. The patterns are formed by a ghost near a saddle-node bifurcation in which a stable traveling wave (node) collides with its critical nucleation mass (saddle). Similar patterns have been observed with fMRI in migraine. Our results support the controversial idea that waves of cortical spreading depression (SD) have a causal relationship with the headache phase in migraine. We suggest a congruence between the prevalence of two subtypes, migraine without aura and migraine with aura, and the statistical properties of the traveling waves. We briefly discuss model-based control and means by which neuromodulation techniques may affect pathways of pain formation.

04:30 PM 05:30 PM

Dicsussion

05:45 PM

Shuttle pick-up from MBI

Thursday, February 7, 2013

Time

Session

08:15 AM

Shuttle to MBI

08:30 AM 09:00 AM

Breakfast

09:00 AM 09:45 AM

Duane Nykamp - What network features have the strongest influence on synchrony?

Duane Nykamp's lecture in what network features have the strongest influence on synchrony?

10:15 AM 11:00 AM

Uri Eden - Tracking dynamic rhythms in the spiking of STN neurons using point process methods

Uri Eden's lecture on tracking dynamic rhythms in the spiking of STN neurons using point process methods.

11:30 AM 12:15 PM

Wilson Truccolo - Microdynamics of Human Focal Seizures

Wilson Truccolo's lecture onMicrodynamics of Human Focal Seizures.

12:30 PM 02:00 PM

Lunch Break

02:00 PM 02:45 PM

Walt Schneider

03:15 PM 04:00 PM

Srikantan Nagarajan

04:30 PM 05:30 PM

Discussion

06:30 PM 07:00 PM

Cash Bar

07:00 PM 07:00 PM

Banquet in the Fusion Room at the Crowne Plaza Hotel

Friday, February 8, 2013

Time

Session

08:15 AM

Shuttle to MBI

08:30 AM 09:00 AM

Breakfast

09:00 AM 09:45 AM

David Grayden - An estimation framework for neural mass models

This work describes a framework for creating patient-specific neural mass models using intracranial electroencephalogram (iEEG) recordings from patients with epilepsy. Neural mass models are used in epilepsy research to relate physiological parameters to iEEG in an attempt to generate hypotheses about the generation and termination of seizures. We will fuse the data and the neural mass model to estimate parameters that specify the shape of post-synaptic potentials, connectivity strength between neural populations, and firing thresholds. A nonlinear version of the Kalman Filter is used with an augmented state-space model to solve the estimation problem. Results from artificial data and patient data show that this is a promising framework.

Ionic concentrations fluctuate significantly during seizures. Substantial increase of extracellular K+ is found during electrically- or pharmacologically-induced paroxysmal activity, along with increase of intracellular Na+. These changes of the ionic concentrations trigger various homeostasis mechanisms such as glial uptake and Na+/K+ ATPase. While Na+/K+ ATPase is one of the most studied proteins, its role in epilepsy remains unclear. Using computational model of in vivo epileptiform activity, we found that increase of intracellular Na+ during epileptiforms leads to significant activation of Na+/K+ ATPase; this increase mediates hyperpolarizing current by Na+/K+ pump that contributes to termination of seizure and postictal depression state. Deficiencies of the Na+/K+ ATPase promote continuous epileptiform activity. In terms of dynamics, the mechanism underlying the smooth transition is due to a safe bifurcation of a homoclinic orbit of a saddle-node equilibrium state terminating the quiescence period of bursting. Overall, our study demonstrated a complex role played by Na+/K+ ATPase in developing of epileptiform activity and may suggest new targets for antiepileptic drugs.

In Parkinson's disease, increased power of oscillations in firing rate has been observed throughout the cortico-basal-ganglia circuit. In particular, the excessive oscillations in the beta range (13-30Hz) have been shown to be associated with difficulty of movement initiation. However, on the basis of experimental data alone it is difficult to determine where these oscillations are generated, due to complex and recurrent structure of the cortico-basal-ganglia-thalamic circuit. This talk will describe a computational model of a subset of basal-ganglia that is able to reproduce experimentally observed patterns of activity. The analysis of the model suggests where and under which conditions the beta oscillations are produced.

Transient localized wave patterns and their application to migraine

Markus Dahlem (Otto-von-Guericke University Magdeburg)

Transient dynamics is pervasive in the human brain and poses challenging problems both in mathematical tractability and clinical observability. We investigate statistical properties of transient cortical wave patterns with characteristic forms (shape, size, duration) in a canonical reaction-diffusion model with mean field inhibition. The patterns are formed by a ghost near a saddle-node bifurcation in which a stable traveling wave (node) collides with its critical nucleation mass (saddle). Similar patterns have been observed with fMRI in migraine. Our results support the controversial idea that waves of cortical spreading depression (SD) have a causal relationship with the headache phase in migraine. We suggest a congruence between the prevalence of two subtypes, migraine without aura and migraine with aura, and the statistical properties of the traveling waves. We briefly discuss model-based control and means by which neuromodulation techniques may affect pathways of pain formation.

A major challenge for the brain is to maintain stability while retaining sufficient flexibility to grow and experience plasticity. The operating state must be such that excessive excitation or insufficient excitation does not result in response to external stimuli. How these opposing constraints reconcile is currently not well understood. We show that after synaptic potentiation, a network of in vitro hippocampal neurons returns to a homeostatic state after widespread increases in firing.

Tracking dynamic rhythms in the spiking of STN neurons using point process methods

Uri Eden (Mathematics and Statistics, Boston University)

Uri Eden's lecture on tracking dynamic rhythms in the spiking of STN neurons using point process methods.

Understanding, Treating, and Curing Psychiatric Illnesses

Flavio Frohlich (Psychiatry, University of North Carolina, Chapel Hill)

David Grayden (Eletrical & Electronic Engineering, The University of Melbourne)

This work describes a framework for creating patient-specific neural mass models using intracranial electroencephalogram (iEEG) recordings from patients with epilepsy. Neural mass models are used in epilepsy research to relate physiological parameters to iEEG in an attempt to generate hypotheses about the generation and termination of seizures. We will fuse the data and the neural mass model to estimate parameters that specify the shape of post-synaptic potentials, connectivity strength between neural populations, and firing thresholds. A nonlinear version of the Kalman Filter is used with an augmented state-space model to solve the estimation problem. Results from artificial data and patient data show that this is a promising framework.

A model of thalamocortical relay neuron and the parkinsonian network

Yixin Guo (Department of Mathematics, Drexel University)

We study a data-driven model of thalamocortical (TC) relay neuron to examine the TC relay responses to an excitatory input train, under inhibitory signals. We first incorporate recording data as inhibitory signals to the TC model to investigate the mechanism underlying deep brain stimulation (DBS) which has been proven clinically effective to relieve motor symptoms for Parkinsonian patients. Then we explore the closed-loop stimulation paradigm using a parkinsonian network model of the basal-ganglia thalamocortical circuit. Our computational results show that the type of stimulation, based on a filtered version of the local field potential, significantly improves the fidelity of thalamocortical (TC) relay. To further understand the different scenarios of TC relay responses, we analyze the entrainment of the TC neuron to periodic signals that alternate between 'on' and 'off', respectively. By exploiting invariant sets of the system and their associated invariant fiber bundles that foliate the phase space, we reduce the 3D TC model to a 2D map. Based on this map, we reproduce the possible scenarios of TC relay responses observed in the data-driven model.

A Framework for Statistical Evaluation of Neural Synchrony

Robert Kass (Department of Statistics, Carnegie-Mellon University)

Several authors have discussed previously the use of loglinear models, often called maximum entropy models, for analyzing spike train data to detect synchrony. The usual loglinear modeling techniques, however, do not allow for time-varying firing rates that typically appear in stimulus-driven (or action-driven) neurons, nor do they incorporate non-Poisson history effects or covariate effects. I will outline a generalization of the usual approach, which combines point process regression models of individual-neuron activity with loglinear models of multiway synchronous interaction (Kass, Kelly, and Loh, 2011, Annals of Applied Statistics; Kelly and Kass, 2012, Neural Computation). I will also describe a method, based on Bayesian control of false discoveries, for assessing the large number of pairs of neurons that are typically examined in a single experiment. Preliminary physiological results come from Utah array recordings in V1.

Multi-scale seizure dynamics

Mark Kramer (Math and Stats, Boston University)

A seizure represents an extreme deviation from normal brain activity. In this talk, we will consider some characteristics of the seizure as observed across spatial and temporal scales in human patients. We will focus specifically on changes in the rhythmic voltage activity, and consider techniques to characterize these changes. We will also discuss a mathematical model consistent with the stereotyped dynamics observed at seizure termination, and use this model to propose what happens dynamically when a seizure fails to self- terminate.

Striatum as a potential source of exaggerated beta rhythms in Parkinsons disease

Michelle McCarthy (Mathematics and Statistics, Boston University)

Prominent beta frequency oscillations appear in the basal ganglia of Parkinsons disease patients. The dynamical mechanisms by which these beta oscillations arise are unknown. Using mathematical models, we show that robust beta frequency rhythms can emerge from inhibitory interactions between striatal medium spiny neurons. Our modeling studies propose that the pathologic beta oscillations in Parkinsons disease may arise as an indirect effect of striatal dopamine loss on the striatal cholinergic system. Experimental testing of our model by infusion of the cholinergic agonist carbachol into normal, mouse striatum induced pronounced, reversible beta oscillations in the striatal local field potential. These results suggest the prominent beta oscillations in Parkinsons disease may bethe result of an exaggeration of normal striatal network dynamics.

Deep brain stimulation (DBS) has emerged as an exciting new possibility for the treatment of neuropsychiatric disorders. Theoretical and experimental evidence suggest that when DBS is applied to neural tissue, it responds with the generation of action potentials in axons. This is especially pertinent to neuropsychiatric DBS applications because they are currently focused on stimulation of sub-cortical white matter. Unfortunately, it is unclear which specific pathways within the white matter are responsible for generating therapeutic benefit from the stimulation. We are attempting to identify those pathways via creation of patient-specific computational models that combine diffusion-tensor tractography, axonal stimulation predictions, and clinical outcome analyses. Our early results from patients with treatment refractory depression suggest that pathways associated with the ventral medial pre-frontal cortex and accumbens play an important role in therapeutic benefit. Identification of specific target pathways for modulation provides opportunities to improve clinical selection of electrode placement and stimulation settings for DBS devices.

Epilepsy

Tay Netoff (Biomedical Engineering, University of Minnesota)

Tay Netoff's lecture on Epilepsy

What network features have the strongest influence on synchrony?

Duane Nykamp (School of Mathematics, University of Minnesota)

Duane Nykamp's lecture in what network features have the strongest influence on synchrony?

Serotonin and the mysteries of depression and SSRI action

Michael Reed (Mathematics, Duke University)

Despite decades of research, the biochemical and neurophysiological causes of depression remain unknown. Furthermore, although selective serotonin reuptake inhibitors (SSRIs) block the reuptake of serotonin and alleviate depression in some patients, it is not clear how or why they work. Mathematical models of serotonin synthesis, release, and reuptake can shed light on the control mechanisms of the serotonin system and suggest hypotheses about the action of SSRIs. We will discuss two of the standard hypotheses and propose a new hypothesis.

Parkinson?s disease has been traditionally thought of as a dopaminergic disease in which cells of the substantia nigra pars compacta (SNc) die. However, accumulating evidence implies an important role for the serotonergic system in Parkinson?s disease in general and in physiological responses to levodopa therapy, the first line of treatment. We use a mathematical model to investigate the consequences of levodopa therapy on the serotonergic system and on the pulsatile release of dopamine (DA) from dopaminergic and serotonergic terminals in the striatum.

We will also ask, and propose an answer to, the question of what serotonin is doing in the striatum anyway?

Leonid Rubchinsky (Department of Mathematical Sciences and Stark Neurosciences Research Institute at the Indiana University School of Medicine, Indiana University--Purdue University)

Motor symptoms of Parkinson's disease have been associated with the synchronized oscillatory activity in the cortico-basal ganglia-thalamic circuits. Here we will present our observations of the patterns of synchronized activity obtained through simultaneous intraoperative recordings of spikes and LFP in the basal ganglia and cortical EEG in parkinsonian patients. We discuss the temporal patterning of the observed synchronized patterning. We show how the synchronization of EEG in motor and prefrontal areas (which can be obtained noninvasively) is predictive of the spike-LFP synchrony in subthalamic nucleus. We also consider the observed phenomena within the framework of mathematical models of cortico-basal ganglia circuits.

On the Therapeutic Mechanisms of Deep Brain Stimulation for Parkinson's Disease: Annihilation or Restoration?

Modeling the neuroprotective role of enhanced astrocyte mitochondrial metabolism during stroke

David Terman (Mathemathics Department, The Ohio State University)

A mathematical model that integrates the dynamics of cell membrane potential, ion homeostasis, cell volume, mitochondrial ATP production, mitochondrial and ER Ca2+ handling, IP3 production and GTP-binding protein coupled receptor signaling is considered. Simulations with the model support recent experimental data showing a protective effect of stimulating astrocytic P2Y1 receptors following cerebral ischemic stroke. The model is analyzed in order to better understand the mathematical behavior of the equations and to provide insights into the underlying biological data. This approach yields explicit formulas determining how changes in IP3-mediated calcium release, under varying conditions of oxygen and the energy substrate pyruvate, affect mitochondrial ATP production, and is utilized to predict rate-limiting variables in P2Y1 receptors enhanced astrocyte protection after cerebral ischemic stroke. This is joint work with C. Diekman, C. Fall and J. Lechleiter.

Microdynamics of Human Focal Seizures

Wilson Truccolo (Neuroscience, Brown University)

Wilson Truccolo's lecture onMicrodynamics of Human Focal Seizures.

Dynamics of healthy and pathological brain - from neuron excitability to network-wide activity and back

Michal Zochowski (Department of Physics and Biophysics Program, University of Michigan)

Ionic concentrations fluctuate significantly during seizures. Substantial increase of extracellular K+ is found during electrically- or pharmacologically-induced paroxysmal activity, along with increase of intracellular Na+. These changes of the i

Motor symptoms of Parkinson's disease have been associated with the synchronized oscillatory activity in the cortico-basal ganglia-thalamic circuits. Here we will present our observations of the patterns of synchronized activity obtained throu

A seizure represents an extreme deviation from normal brain activity. In this talk, we will consider some characteristics of the seizure as observed across spatial and temporal scales in human patients. We will focus specifically on changes in the

The MBI receives major funding from the National Science Foundation Division of Mathematical Sciences and is supported by The Ohio State University.
If you have trouble accessing this page and need to request an alternate format, contact webmaster@mbi.osu.edu